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Display information for equation id:math.1255.137 on revision:1255

* Page found: Das d'Alembertsche Prinzip (eq math.1255.137)

Occurrences on the following pages:

Lagrangegleichungen 2. Art Eq: math.1508.26

Hash: 671c5f754b6c36fd02da29e702ba5b23

TeX (original user input):

\begin{align}
  & \vec{L}=m\vec{v}\times \vec{r} \\
 & {{{\vec{L}}}_{o}}=m{{\omega }_{o}}^{{}}{{R}_{o}}^{2}\quad {{v}_{o}}={{\omega }_{o}}{{R}_{o}}\quad {{r}_{o}}={{R}_{o}} \\
 & andererseits: \\
 & {{\omega }_{o}}=\frac{con\tilde{s}}{{{({{R}_{o}})}^{2}}} \\
 & \Rightarrow \omega =\frac{con\tilde{s}}{{{({{R}_{o}}-ct)}^{2}}}\Rightarrow con\tilde{s}=\frac{{{{\vec{L}}}_{o}}}{m} \\
 & \omega =\frac{{{{\vec{L}}}_{o}}}{m{{({{R}_{o}}-ct)}^{2}}}=\dot{q} \\
\end{align}

TeX (checked):

{\begin{aligned}&{\vec {L}}=m{\vec {v}}\times {\vec {r}}\\&{{\vec {L}}_{o}}=m{{\omega }_{o}}^{}{{R}_{o}}^{2}\quad {{v}_{o}}={{\omega }_{o}}{{R}_{o}}\quad {{r}_{o}}={{R}_{o}}\\&andererseits:\\&{{\omega }_{o}}={\frac {con{\tilde {s}}}{{({{R}_{o}})}^{2}}}\\&\Rightarrow \omega ={\frac {con{\tilde {s}}}{{({{R}_{o}}-ct)}^{2}}}\Rightarrow con{\tilde {s}}={\frac {{\vec {L}}_{o}}{m}}\\&\omega ={\frac {{\vec {L}}_{o}}{m{{({{R}_{o}}-ct)}^{2}}}}={\dot {q}}\\\end{aligned}}

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MathML (4.337 KB / 571 B) :

\begin{aligned} \vec{L} = m \vec{v} \times \vec{r} \\ {\vec{L}}_{o} = m {ω_{o}}^{} {R_{o}}^{2} v_{o} = ω_{o} R_{o} r_{o} = R_{o} \\ a n d e r e r s e i t s : \\ ω_{o} = \frac{c o n \tilde{s}}{{(R_{o})}^{2}} \\ \Rightarrow ω = \frac{c o n \tilde{s}}{{(R_{o} - c t)}^{2}} \Rightarrow c o n \tilde{s} = \frac{{\vec{L}}_{o}}{m} \\ ω = \frac{{\vec{L}}_{o}}{m {(R_{o} - c t)}^{2}} = \dot{q} \end{aligned}

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Identifiers

$\vec{L}$

$m$

$\vec{v}$

$\vec{r}$

${\vec{L}}_{o}$

$m$

$ω_{o}$

$R_{o}$

$v_{o}$

$ω_{o}$

$R_{o}$

$r_{o}$

$R_{o}$

$a$

$n$

$d$

$e$

$r$

$e$

$r$

$s$

$e$

$i$

$t$

$s$

$ω_{o}$

$c$

$o$

$n$

$\tilde{s}$

$R_{o}$

$ω$

$c$

$o$

$n$

$\tilde{s}$

$R_{o}$

$c$

$t$

$c$

$o$

$n$

$\tilde{s}$

${\vec{L}}_{o}$

$m$

$ω$

${\vec{L}}_{o}$

$m$

$R_{o}$

$c$

$t$

$\dot{q}$

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